Route determination method, controller, and routing system comprising controller

ABSTRACT

A time-space network including a set of state nodes and a set of state transition edges each of which connects between the state nodes, is generated. Each of the state nodes represents a state in which a vehicle is present at a certain point node at a certain time. State transition costs increasing according to a difference of time corresponding to before or after transition and arrival time are defined. In the time-space network, by using the Dijkstra algorithm, a minimum cost transition path in which a sum of the state transition costs is minimum among paths from a starting point state node to any of the state nodes indicating that the vehicle is present at an arrival point is obtained. The starting point state node represents a state that the vehicle is present at a departure point at a reference time. The route and the timing of the vehicle are determined based on the minimum cost transition path.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of priority to Japanese PatentApplication No. 2019-095742 filed on May 22, 2019. The entire contentsof this application are hereby incorporated herein by reference.

BACKGROUND OF THE INVENTION 1. Field of the Invention

At least one preferred embodiment of the present invention relates tothe determination of routing and timing for automated guided vehicles toperform automatic travel.

2. Description of the Related Art

For example, in transport systems such as semiconductor manufacturingplants, in order to improve efficiency and productivity ofsemiconductors and processing devices, etc., JIT (Just In Time)performance is required to deliver materials just in time to bedelivered in time for a designated time. Japanese Patent No. 4,782,194discloses a routing method used in this type of transport system.

In the routing method used in the transport system of Japanese PatentNo. 4,782,194, a schedule of transport scenarios is generated. When adeviation from the predefined schedule occurs, a rerouting is carriedout so as to realize JIT transport.

In the configuration of Japanese Patent No. 4,782,194, for example, in alarge semiconductor manufacturing plant or the like, in which the numberof vehicles is several tens to hundreds, or thousands, it is required togenerate the schedule so that each of the vehicles does not interferewith a large number of the other vehicles during traveling. Therefore,the efficiency of the schedule is low, and there is a high possibilitythat JIT transport is not realized.

SUMMARY OF THE INVENTION

Preferred embodiments of the present invention determine routing andtiming of vehicles having good JIT performance with good efficiency.

A first preferred embodiment of the present invention provides adetermination method of routing for automated guided vehicles, in whicha route and timing of a vehicle that performs automatic traveling aredetermined. In the method, a first graph is prepared. The first graphrepresents the routes along which the vehicle can travel. The firstgraph includes a set of point nodes, and inter-point edges in each ofwhich connects between the point nodes. Each of a departure point node,which is a departure point of the vehicle, and an arrival point node,which is an arrival point of the vehicle, can be selected from the pointnodes in the first graph. When a departure time at which the vehicle isto depart from the departure point node and arrival time at which thevehicle is to arrive at the arrival point node are designatedrespectively, a second graph is generated. The second graph represents aprocedure for the vehicle traveling from the departure point node to thearrival point node. The second graph includes a set of state nodes, anda set of state transition edges connected between the state nodes. Eachof the state nodes represents a state in which the vehicle is present ata certain point node at a certain time. Each of the state transitionedges connects between the state nodes. The state transition edgesinclude a vehicle staying edge and a vehicle traveling edge. The vehiclestaying edge represents that the vehicle present at a certain point nodeat a certain time stays at the certain point node until a later time.The vehicle traveling edge indicates that the vehicle present at acertain point node at a certain time travels to each of the other pointnodes connected to the certain point node via the inter-point edge at alater time. The vehicle traveling edge is defined for each of the pointnodes of destination. It is presupposed that the state node representinga state in which the vehicle is present at the departure point node at areference time is called a starting point state node, the second graphis generated originating from the starting point state node. In each ofthe state transition edges, a state transition cost is defined. Thestate transition cost increases according to a difference of time beforeor after a transition indicated by the state transition edge and thearrival time. In the second graph, by using the Dijkstra algorithm, aminimum cost path is obtained. The minimum cost path is the path inwhich a sum of the state transition costs is minimum among the pathsfrom the starting point state node to any of the state nodes indicatingthat the vehicle is present at the arrival point node. The route and thetiming of the vehicle are determined based on the minimum cost path.

As a result, it is possible to efficiently obtain the minimum cost pathfor travel of the vehicle from the designated departure point to thearrival point. Additionally, the state transition cost in the statetransition edge is set according to a time difference corresponding tobefore or after the transition indicated by the state transition edgeand the arrival time. Therefore, it is possible to generate a minimumcost path considering the JIT performance so that the vehicle arrives atthe designated point at the designated time.

In the routing determination method, it is preferable to perform thefollowing. The state transition cost is set to be larger when the timecorresponding to before or after the transition indicated by the statetransition edge is later than the arrival time than when it is earlier,even if the time difference is the same.

As a result, it is possible to greatly reduce the possibility that apath to arrive at the arrival point at a time later than the designatedtime is determined as the minimum cost path.

In the routing determination method, it is preferable to perform thefollowing procedure. The state transition cost is obtained based on thetotal cost including an earliness cost, a tardiness cost, and a stayingcost. The earliness cost is added if the time corresponding to before orafter the transition indicated by the corresponding state transitionedge is earlier than the arrival time. The tardiness cost is added ifthe time corresponding to before or after the transition indicated bythe corresponding state transition edge is later than the arrival time.The staying cost is added when the vehicle stays at any of the pointnodes. Each of the first parameter for weighting the earliness cost, asecond parameter for weighting the tardiness cost, and a third parameterfor weighting the staying cost can be specified.

By appropriately specifying the first parameter, the second parameter,and the third parameter, it is possible to determine a travelingschedule corresponding to the degree of importance with respect to theJIT performance and the transport efficiency respectively.

In the routing determination method, it is preferable that a distancebetween real points represented by the point nodes corresponds to atravel distance of per unit time of the vehicle.

As a result, the computation of the state transition cost can befacilitated.

In the routing determination method, it is preferable to perform thefollowing. The route and the timing are simultaneously determined byobtaining the minimum cost path for each of a set of the vehicles inwhich each of the departure point node, the arrival point node, thedeparture time, and the arrival time are designated. If interferenceoccurs between the vehicles in a case where each of the vehicles travelsin accordance with the route and the timing, the route and the timingare determined again by re-obtaining the minimum cost path. The minimumcost path is re-obtained after increasing the state transition cost ofthe state transition edge corresponding to the interference.

As a result, the collision avoidance is able to be easily determinedwhile considering the JIT performance.

In the routing determination method, it is preferable to perform thefollowing. In the method for obtaining the minimum cost path, aniteration is repeated after an initial step. In the initial step, in thesecond graph, the starting point state node is set to a fixed node and afixed cost of the starting point state node is set to a predeterminedvalue. The iteration includes a first step, a second step, a third step,and a fourth step. In the first step, neighbor state nodes are obtained.Each of the neighbor state nodes is a state node which is not set to afixed node, is adjacent to any fixed node, and is connected to the fixednode via the state transition edge. In the second step, with respect tospecific neighbor state nodes, the state transition cost cumulativevalues for reaching the neighbor state nodes are obtained. The specificneighbor state nodes are neighbor state nodes, each of which is adjacentto a new-fixed node and is connected to the new-fixed node via the statetransition edge. The new-fixed node is a node that has newly become thefixed node in the initial step or in the previous iteration. The statetransition cost cumulative value is obtained by adding the cost of thestate transition edge to the fixed cost of the new-fixed node. In thethird step, with respect to each of the neighbor state nodes, a statetransition cost cumulative best value is obtained. The state transitioncost cumulative best value is the state transition cost cumulative valuethat is best among the state transition cost cumulative values obtainedby the second step in the iteration from the first time to the present.In the fourth step, the neighbor state node with the smallest statetransition cost cumulative best value obtained by the third step is setto the fixed node, and the state transition cost cumulative best valueis set to the fixed cost of the fixed node. The fixed node and the fixedcost are sequentially obtained by repeating the iteration. A path inwhich the fixed cost is the smallest among the paths reaching the statenode indicating that the vehicle is present at the arrival point node isobtained as the minimum cost path.

As a result, the minimum cost path can be searched efficiently.Additionally, for example, a traveling schedule that takes into accountthe balance between just-in-time performance and the total completiontime, which are usually in a trade-off relationship, are able to bedetermined.

A second preferred embodiment of the present invention provides acontroller having the following configuration. The controller determinesthe route and the timing of the vehicle using the routing determinationmethod.

As a result, it is possible to determine efficiently the route and thetiming suitable for JIT performance. This effect is particularlysuitable in a transport system of a large-scale plant, a large automaticstocker, and the like, having a large number of the vehicles.

A third preferred embodiment of the present invention provides a routingsystem having the following configuration. The transport system includesthe controller and a plurality of traveling devices. A plurality of thetraveling devices perform automatic routing according to the route andthe timing determined by the controller.

As a result, it is possible to efficiently determine the route and thetiming with respect to a plurality of the travel devices. Thus, theoverall efficiency of the transport system is able to be improved.

The above and other elements, features, steps, characteristics andadvantages of the present invention will become more apparent from thefollowing detailed description of the preferred embodiments withreference to the attached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic view showing a configuration of a plant using atransport system according to a preferred embodiment of the presentinvention.

FIG. 2 is a block diagram showing a configuration of the transportsystem of FIG. 1.

FIG. 3 is a diagram showing an example of a route graph.

FIG. 4 is a diagram showing a time-space network and showing a minimumcost transition path for arriving at a designated unloading position ata second designated time.

FIG. 5 is a diagram showing a state that a starting point state node isset to a fixed node in the initial step for computing a minimum costtransition path by the Dijkstra algorithm.

FIG. 6 is a diagram showing a situation that state transition costcumulative values of neighbor state nodes are obtained from the state ofFIG.5.

FIG. 7 is a diagram showing a situation that fixed nodes and fixed costsare obtained from the state of FIG. 6.

FIG. 8 is a diagram showing a situation that fixed nodes and fixed costsare further obtained from the state of FIG. 7.

FIG. 9 is a diagram showing a state that a minimum cost transition pathis obtained by the Dijkstra algorithm.

FIG. 10 is a diagram showing an avoidance route obtained byre-computation after increasing a state transition cost to avoidcollision.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Next, preferred embodiments of the present invention will be describedwith reference to the drawings. FIG. 1 is a schematic view showing aplant 10 using a transport system 100 according to a preferredembodiment of the present invention.

The transport system (traveling system) 100 according to a preferredembodiment of the present invention, for example, as shown in FIG. 1, isprovided in a semiconductor manufacturing plant 10 or the like having aplurality of processing devices 1. The transport system 100 is anautomatic transport system for transporting the material such as FOUP(Front Opening Unify Pod) or the like. The transport system 100 includesa set of traveling carriages (vehicles as traveling devices) 2 and atraveling carriage manager (controller) 3, as shown in FIG. 2.

The processing device 1 is a device that performs various processes toproduce semiconductors. The plant 10 having the transport system 100 isprovided with a variety of facilities in place of the processing device1 or in addition to the processing device 1. For example, a storagedevice, such as an automatic stocker, a stacker rack, or the like, canbe placed. The automatic stocker can store a plurality of FOUP. In thestacker rack, a large number of storage spaces capable of storing loadssuch as parts or materials are provided.

The traveling carriage 2 is a transport device that travels along rails4 to transport a load or loads automatically between the processingdevices 1. The rails 4 are made of, for example, a guiding tape such asmagnetic tape or the like, or a bar code or the like, attached to thefloor surface. The rails 4 may be a guide provided on at least one ofthe traveling carriage 2 side and the rails 4 side so that runningwheels (not shown) of the traveling carriage 2 run along the rails 4.Further, the rail 4 may be, for example, a guide or the like which issuspended from the ceiling of the plant 10.

The traveling carriage 2 is provided with a polyarticular robotic arm orthe like (not shown). The robotic arm can perform loading and unloading.As the traveling carriage 2, for example, AGV (Automated Guided Vehicle)or OHT (Overhead Hoist Transfer) can be used.

Each of the traveling carriages 2 performs automatic travel according toa traveling schedule based on a transport task allocated by a travelingcarriage manager 3. The traveling carriage manager 3 will be describedlater. Specifically, the traveling carriage 2 transports a designatedload from a designated loading portion P1 to an designated unloadingposition P2. The automatic travel includes a pause for collisionavoidance, and the like.

The transport task is a transport order for transporting designatedload, obtained by loading at a designated loading position P1, to thedesignated unloading position P2. In other words, the transport taskincludes a position information of the designated loading P1 and thedesignated unloading position P2, and the like. In addition, thetransport task may include an identification information of the load(designated load) as a subject for transporting from the designatedloading position P1 to the designated unloading position P2.

In addition to the above, the transport task of this preferredembodiment includes a first designated time and a second designatedtime. The first designated time is a time specified with respect to thetraveling carriage 2 as a time to arrive at the designated loadingposition P1. The second designated time is a time specified with respectto the traveling carriage 2 as a time to arrive at the designatedunloading position P2. In this specification, the second designated timeT_(set) may be referred to as an arrival time.

The traveling schedule is a schedule with respect to a route and atiming in automatic travel of the traveling carriage 2. The travelingschedule is developed as the traveling carriage manager 3 allocates thetransport task to the traveling carriage (or attempts to allocate).

The traveling carriage 2 includes a carriage controller 20 and acarriage signal transmitter/receiver 21, as shown in FIG. 2.

The carriage controller 20 may be or include a known computer. Thecarriage controller 20 includes a CPU (Central Processing Unit), a ROM(Read Only Memory), a RAM (Random Access Memory), an HDD (Hard DiskDrive), and the like, which are not shown.

The carriage controller 20 controls a load transfer operation, automatictravel, and the like. The load transfer operation is performed by atransfer mechanism such as a polyarticular robotic arm or hoist (notshown) provided with the traveling carriage 2. Automatic travel isperformed by travel mechanism (not shown) provided with the travelingcarriage 2.

The carriage signal transmitter/receiver 21 is configured to enableradio communication with the traveling carriage manager 3. Any radiocommunication method can be used. For example, a wireless LAN can beused. The carriage signal transmitter/receiver 21 can transmitself-position of the traveling carriage 2 to the traveling carriagemanager 3 by radio communication. The carriage signaltransmitter/receiver 21 can also receive the transport task allocated,and related information corresponding to the transport task, or thelike. As the radio communication method, communication using leakagefeeder wire or leakage coaxial cable can also be used.

The traveling carriage manager 3 may be or include, for example,similarly to the carriage controller 20 described above, a knowncomputer. The traveling carriage manager 3 includes a CPU (CentralProcessing Unit), a ROM (Read Only Memory), a RAM (Random AccessMemory), an HDD (Hard Disk Drive), and the like (not shown).

The traveling carriage manager 3 allocates each of a plurality of thetransport tasks to any of a set of the traveling carriages 2 which aremanaged. The transport tasks are supplied from a production manager,etc. of the upper layer (not shown) to the traveling carriage manager 3.Then, the traveling carriage manager 3 determines a traveling schedulecorresponding to the allocated transport task.

With respect to the transport task, the traveling carriage manager 3determines a traveling schedule in which the traveling carriage 2 willtravel from the departure position to the designated loading position P1and a traveling schedule in which it will travel from the designatedloading position P1 (departure point) to the designated unloadingposition P2 (arrival point), respectively.

Here, the departure position is the current position of the travelingcarriage 2 at a task start time which is pre-specified. As the taskstart time, for example, a time in which the traveling carriage 2receives the transport task from the traveling carriage manager 3 can beset. However, this is not limiting. The task start time can be set toany time after receiving the transport task.

The traveling carriage manager 3 stores a route graph (a first graph)generated in advance. The prepared route graph is an abstraction ofroutes that the traveling carriage 2 can travel and is represented as agraph. The route graph includes a set of point nodes and inter-pointedges. Each of the inter-point edges connects between the point nodes.By the route graph, it is possible to search one or multiple routes fortravel from one point to another point. The departure position, thedesignated loading position P1 and the designated unloading position P2of the traveling carriage 2 are all specified in the form of the pointnode in the route graph.

Real points indicated by a set of the point nodes are located side byside on the rails 4 with distance intervals corresponding to traveldistance of per unit time of the traveling carriage 2, for example.However, this is not limiting. The point node may be set to indicate,for example, a position of each of the respective processing devices 1.The real points indicated by a set of the point nodes do not have to beset at equal intervals. The real points can be set at non-equalintervals depending on the acceleration/deceleration of the travelingcarriage 2. The points are preferably defined by intervals correspondingto unit time because it facilitates computation of the state transitioncost to be described later.

Each of the inter-point edges has information of a travel cost. In theroute graph, each of the travel costs is defined as a time required forthe traveling carriage 2 to travel from one point node to another pointnode among the point nodes connected by the inter-point edges. By usinginformation of the travel cost, it is possible to obtain a time requiredfor travel from one point to another point by computation.

FIG. 3 shows an example of the route graph. In FIG. 3, the point node isdepicted as a circled numeral. The numeral indicates a number thatuniquely identifies the point node. In the following, the circlednumeral indicating the point node may be represented by a parenthesizednumber, for example, point node (1). Each of inter-point edges isrepresented as an arrow connecting two point nodes.

In this preferred embodiment, the route graph is represented as adirected graph because the routes of rails 4 are one-way. If adouble-sided passage of rails 4 is available, the route graph can alsobe represented by an undirected graph.

In the following, as an example, the case where the point node (20)shown in FIG. 3 is the departure position of the traveling carriage 2,the point node (1) is the designated loading position P1, and the pointnode (5) is the designated unloading position P2 will be described.

The traveling carriage manager 3 first determines a traveling schedulefrom the departure position to the designated loading position P1 suchthat the traveling carriage 2 arrives from a departure position to thedesignated loading position P1 in the shortest time. The travelingschedule can be obtained, for example, by computation of the shortestpath from the point node (20) of the departure position to the pointnode (1) of the designated loading position P1 by the Dijkstra'salgorithm or A* algorithms or the like in the route graph.

The Dijkstra's algorithm is a shortest path finding method. In theDijkstra's algorithm, the shortest path to each of the point nodes isdetermined one by one from the point node (20) as a starting pointtowards the periphery, and a search range is gradually expanded to thepoint node (1) as an ending point. Since the Dijkstra algorithm is wellknown, detailed descriptions thereof are omitted.

Next, the traveling carriage manager 3 uses a traveling scheduledetermination method (a routing determination method) to determine atraveling schedule for the traveling carriage 2 to travel from thedesignated loading position P1 to the designated unloading position P2.The traveling schedule determination method of this preferred embodimentcan determine a traveling schedule of the traveling carriage 2 such thatthe traveling carriage 2 arrives at the designated unloading position P2just in time for the second designated time T_(set). That is, it ispossible to determine a traveling schedule considering the JITperformance.

In the transport task allocated to the traveling carriage 2, the pointnode representing the designated loading position P1, which is adeparture point node, and the point node representing the designatedunloading position P2, which is an arrival point node, are arbitrarilyselected. In the following, as an example, a case where the departurepoint node is designated in the point node (1) of FIG. 3 and the arrivalpoint node is designated in the point node (5) of FIG. 3 will bedescribed.

The traveling carriage manager 3 generates a time-space network (asecond graph) to obtain a minimum cost transition path (a minimum costpath) described later. The time-space network compositely represents aposition and a timing of the traveling carriage 2.

The time-space network includes, as shown in FIG. 4, for example, a setof state nodes and a set of state transition edges. The state node isrepresented by a circle in FIG. 4. The state node represents a statethat the traveling carriage 2 is present at a certain point node at acertain time. In FIG. 4, a numeral in the circle indicates the number ofthe point node. In FIG. 4, the positions of the state nodes (circles)are arranged in such a way that the older the corresponding time is, themore to the left it is positioned, and the newer the corresponding timethe more to the right it is positioned.

Each of the state nodes represents a combination of the position of thetraveling carriage 2 and the time. For example, the eight state nodes inthe bottom row of FIG. 4 represent each of the states in which thetraveling carriage 2 is present at the point node (1) at each time.

Each of the state transition edges connects between the state nodes. Thestate transition edge indicates that the state of traveling carriage 2can transition from a state node connected prior to the state transitionedge to a state node connected after the state transition edge.

In the time-space network, the state transition edges include a carriagestaying edge (a vehicle staying edge) 5 and a carriage traveling edge (avehicle traveling edge) 6 shown in FIG. 4.

The carriage staying edge 5 is an edge connecting two state nodes. Thetwo state nodes indicate the same point node and the two times at whichthey are different by a unit time. In FIG. 4, the carriage staying edge5 is represented by a horizontal arrow.

The carriage traveling edge 6 is an edge connecting two state nodes. Thetwo state nodes indicate different point nodes and the two times atwhich they are different by a unit time. In FIG. 4, the carriagetraveling edge 6 is represented by a diagonal arrow.

Time cannot be turned back. Thus, any state transition edge isrepresented as an arrow from the state node in which the time is theprevious time to the state node in which the time is later time by aunit time. As a result, the time-space network is a directed graph.

The state node located at the bottom leftmost position in FIG. 4represents a state that the traveling carriage 2 is present at the pointnode (1) at the departure time (e.g., time t=0). The departure time is atime at which the traveling carriage completes loading at the designatedloading position P1 and departs from the designated loading position P1.

The time of t=0 may be referred to as a reference time in the followingsince it is used as a reference for time. In the following, in order tospecify each of the state nodes, it may also be expressed as [t=0, n=1]for example, by using time t and the number n of the point node at whichthe traveling carriage 2 is present.

The state node [t=0, n=1], in other words, the bottom leftmost statenode of FIG. 4, can be considered as the origin of various transitionsof the state with respect to travel of the traveling carriage 2.Therefore, in the following, this state node is sometimes referred to asa starting point state node. The time-space network is generated toexpand from the starting point state node as its origin.

The starting point state node represents the state of the travelingcarriage 2 is present at the point node (1) at time t=0. There are twopossible transitions from this state, the traveling carriage 2 stays atthe point node (1) or travels to the point node (2).

If the traveling carriage 2 stays at the point node (1), the statetransitions from the starting point state node [t=0, n=1] to the statenode [t=1, n=1] along the carriage staying edge 5. The state node [t=1,n=1] indicates the state of the traveling carriage 2 is present at thepoint node (1) at a time of t=1.

If the traveling carriage 2 travels from the point node (1) to the pointnode (2), the state transitions from the starting point state node [t=0,n=1] to the state node [t=1, n=2] along the carriage traveling edge 6.The state node [t=1, n=2] indicates the state of the traveling carriage2 is present at the point node (2) at a time of t=1.

Thus, each of the state transition edges represents a state transitionassociated with the passage of a unit time.

As shown in the route graph of FIG. 3, if the traveling carriage 2travels from the point node (1), there is no other option but to go tothe point node (2). Similarly, in each of the point nodes (2)-(4), thereis only one option (one point node) of destination when the travelingcarriage 2 is travel from the point node. Therefore, the time-spacenetwork in this case has a simple shape in which two branches consistingof one carriage traveling edge 6 and one carriage staying edge 5 arerepeated, as shown in FIG. 4.

On the other hand, for example, if the traveling carriage 2 travels fromthe point node (22), any one of the point node (8) and the point node(23) can be selected as a destination. When the destination branches inthis manner, a number of the carriage traveling edges 6 are generated inthe time-space network according to the point nodes of destination.Therefore, the time-space network is more complex than the example shownin FIG. 4. Which point node the traveling carriage 2 can travel from thepresent point node can be easily obtained by referring to the routegraph.

In generating the time-space network, the traveling carriage manager 3calculates a state transition cost d_(σaσb) at each of the statetransition edges using the expression (1) below.

$\begin{matrix}{d_{\sigma_{a}\sigma_{b}} = \left\{ \begin{matrix}{{{\alpha \; {\max \left( {0,{T_{set} - t_{\sigma_{b}}}} \right)}} + {\gamma \; {\max \left( {0,{t_{\sigma_{b}} - T_{set}}} \right)}}},} & {n_{\sigma_{a}} \neq n_{\sigma_{b}}} \\{{{\beta \; t_{\sigma_{b}}} + {\gamma \; {\max \left( {0,{t_{\sigma_{b}} - T_{set}}} \right)}}},} & {n_{\sigma_{a}} = n_{\sigma_{b}}}\end{matrix} \right.} & (1)\end{matrix}$

Here, σ is the state node indicating the state in which the travelingcarriage 2 is present at the point node (n) at time t. n_(σ), is thenumber of the point node indicated by the state node. t_(σ) is the timeindicated by state node. σ_(a) is the state node whose time is the older(before the transition) of the two state nodes connected by the statetransition edge, and σ_(b) is the state node whose time is the newer(after the transition). T_(set) is a time (a second designated time)specified as the time to arrive at the designated unloading position P2.α is a first parameter related to an earliness cost, which will bedescribed later. γ is a second parameter related to a tardiness cost,which will be described later. β is a third parameter related to astaying cost, which will be described later.

As shown in the expression (1) above, the state transition cost of eachof the state transition edges is set according to a difference in thetime t_(σb) corresponding to after the transition indicated by the statetransition edge and the second designated time T_(set).

The upper expression of the expression (1) is used to calculate thestate transition cost in the carriage traveling edge (a diagonal arrowin FIG. 4) included in the state transition edges.

The upper expression of the expression (1) contains the terms shown inthe expression (2) and the expression (3) below.

α max(0, T_(set)−t_(σ) _(b) )   (2)

The term in the expression (2) is a term that calculates a cost (anearliness cost) for negatively evaluating that the timing of thetraveling carriage 2 is too early. The earliness cost term is zero iftime t_(σb) when the traveling carriage 2 travels to any point node isafter the second designated time T_(set), otherwise it is positive. Theearliness cost is calculated so that the earlier time t_(σb) when thetraveling carriage 2 travels in any point node is than the seconddesignated time T_(set), the higher it is. The first parameter αincluded in the expression (2) is for weighting and can be appropriatelyspecified.

γmax(0, t_(σ) _(b) −T_(set))   (3)

The term in the expression (3) is a term that calculates a cost (atardiness cost) for negatively evaluating that the timing of thetraveling carriage 2 is too late. The tardiness cost term is zero iftime t_(σb) when the traveling carriage 2 travels to any point node isbefore the second designated time T_(set), otherwise it is positive. Thetardiness cost is calculated so that the later time t_(σb) when thetraveling carriage 2 travels in any point node is than the seconddesignated time T_(set), the higher it is. The second parameter γincluded in the expression (3) is for weighting and can be appropriatelyspecified.

The lower expression of the above expression (1) is used to calculatethe state transition cost in the carriage staying edge 5 (a horizontalarrow in FIG. 4) included in the state transition edges.

The lower expression of the expression (1) contains the terms shown inthe expression (4) below and the expression (3) above.

βt_(σ) _(b)   (4)

The term in the expression (4) is a term that calculates a cost (astaying cost) for negatively evaluating that a traveling carriage 2 isstaying (in other words, the traveling carriage 2 does not contribute totransporting of the load). This term representing the staying cost iscalculated so that when the traveling carriage 2 stays at any pointnode, the later time t_(σb) at that timing, the higher it is. Thestaying cost encourages efficient use of the traveling carriage 2 fortransporting a load. The third parameter included in the expression (4)is for weighting and can be appropriately specified.

If the traveling carriage 2 travels from one point node to another, thestate transition cost associated with this state transition (the statetransition represented by the carriage traveling edge 6) is a sum of theearliness cost and the tardiness cost. On the other hand, if thetraveling carriage 2 stays at a certain point node, the state transitioncost associated with this state transition (the state transitionrepresented by the carriage staying edge 5) is a sum of the tardinesscost and the staying cost.

Comprehensively considering the above, when traveling from thedesignated loading position P1 to the designated unloading position P2,if it proceeds as shown in the thick arrow of FIG. 4, the tardiness costcan be zeroed and the staying cost and the earliness cost can bereduced. That is, the traveling carriage 2 does not travel much from thedesignated loading position P1 (the point node (1)) until a tight timingsuch that the arrival at the designated unloading position P2 (the pointnode (5)) is not late for the second designated time T_(set). Then, thetraveling carriage starts moving. The traveling carriage 2 arrives atthe designated unloading position P2 exactly at the second designatedtime T_(set).

Hereinafter, in the time-space network, the state node [t=0, n=1] may bereferred to as a start state node. The state node [t=any, n=5] may bereferred to as a goal state node.

The start state node is equal to the starting point state node. Thestart state node is a state node representing the state that thetraveling carriage 2 is present at the designated loading position P1 attime t=0. The goal state node is a state node representing the statethat the traveling carriage 2 is present at the designated unloadingposition P2 at any time t. In FIG. 4, the start state node is denoted byS and the goal state node is denoted by G. Each path from the startstate node S to any of the goal state nodes G is a path that can realizetransporting of the load from the designated loading position P1 to thedesignated unloading position P2, putting aside the timing.

In the traveling schedule determination method of this preferredembodiment, a path (minimum cost path) in which a sum of the statetransition costs is minimum among paths from the start state node S toany of the goal state nodes G is obtained using the Dijkstra algorithm.Although it depends on the setting of the first parameter α, the secondparameter γ, and the third parameter β, the path shown in thick arrow inFIG. 4 is a path that is likely to be the minimum cost path.

By appropriately setting each of the first parameter α, the secondparameter γ, and the third parameter β, the traveling scheduledetermination method of this preferred embodiment can determine atraveling schedule suitable only for the JIT performance or a travelingschedule suitable only for transport efficiency (i.e., a totalcompletion time required for automatic travel corresponding to a certaintransport task). Further, the method can determine an optimum travelingschedule considering both the JIT performance and transport efficiency(the total completion time) with different weights. For example, bysetting the second parameter y to be larger than the first parameter aand the third parameter the traveling schedule determined emphasizesavoiding delay in the arrival of the load.

Next, a method of obtaining the above-mentioned minimum cost transitionpath by the Dijkstra algorithm will be described in detail. The methodincludes an initial step and an iteration. In the following, as anexample, the case where each of the state transition costs is defined asindicated by a number in the respective arrow in FIG. 5 will bedescribed. To avoid the complexity of the description, the statetransition costs shown in FIG. 5 are simple integer values for the onlyexplanation which does not comply with the expression (1) above.

In the initial step, with respect to the time-space network created asdescribed above, the traveling carriage manager 3 sets the startingpoint state node (the state node [t=0, n=1]) to a fixed node. Further,the traveling carriage manager 3 sets a fixed cost of the starting pointstate node to a predetermined value (e.g., 0). This state is shown inFIG. 5. In FIG. 5 and subsequent figures, the fixed node is indicated byhatching, and the fixed cost is indicated as a square-shaped numericalvalue.

After performing the initial step as described above, the travelingcarriage manager 3 performs an iteration including a first step, asecond step, a third step, and a fourth step below.

When the iteration is started, the traveling carriage manager 3determines neighbor state nodes (the first step). The neighbor statenode is the state node which is not the fixed node, is adjacent to thefixed node, and is connected to the fixed node by the state transitionedge.

In the state of FIG. 5, there is only one fixed node, i.e., [t=0, n=1].Thus, when the first step is performed at this state, the neighbor statenodes are the two state nodes, i.e., [t=1, n=1] and [t=1, n=2].

Then, in the neighbor state nodes determined, the traveling carriagemanager 3 obtains state transition cost cumulative values reaching theneighbor state nodes each of which is adjacent to a new-fixed node andis connected to the new-fixed node by the state transition edge (thesecond step). The new-fixed node is a node which has become the fixednode newly in the previous iteration (in the first iteration, has becomethe fixed node in the initial step).

In the second step, the traveling carriage manager 3 obtains the statetransition cost cumulative value to each of the neighbor state nodeswhich has become subject as described above. The state transition costcumulative value is obtained by adding the state transition cost (cost)in the state transition edge connecting the new-fixed node and theneighbor state node to the fixed cost in the new-fixed node.

The results of the second step are shown in FIG. 6. The fixed cost ofnew-fixed node [t=0, n=1] is 0. Therefore, the state transition costcumulative value of the neighbor state node [t=1, n=1] is 0 plus thestate transition cost 7, resulting in 7. The state transition costcumulative value of the neighbor state node [t=1, n=2] is 0 plus thestate transition cost 2, resulting in 2. The state transition costcumulative values are shown in the underlined number in FIG. 6.

Next, for each of the neighbor state nodes, the traveling carriagemanager 3 obtains a state transition cost cumulative best value (thethird step). The state transition cost cumulative best value is a statetransition cost cumulative value that is best (value is minimum) amongthe state transition cost cumulative values obtained by the second stepin the iteration from the first time to this time.

In the state of FIG. 6, the state transition cost cumulative value ofneighbor state node [t=1, n=1] is 7. Since it is a first time iteration,for the neighbor state node, this state transition cost cumulative valueis minimum. Therefore, the state transition cost cumulative best valueof the neighbor state node is 7. Regarding the neighbor state node [t=1,n=2], considering similarly as above, the state transition costcumulative best value is 2.

Next, the traveling carriage manager 3 sets the neighbor state node withthe smallest state transition cost cumulative best value obtained asabove among the neighbor state nodes to a fixed node, and sets the statetransition cost cumulative best value of the neighbor state node as itsfixed cost (the fourth step).

The results of the fourth step are shown in FIG. 7. The state transitioncost cumulative best value, which is minimum, is 2. Therefore, the statenode [t=1, n=2] newly becomes the fixed node, and its fixed cost is setto 2.

The traveling carriage manager 3 sequentially obtains the fixed node andthe fixed cost one by one by repeating the iteration.

From the state of FIG. 7, the results of the second step, the thirdstep, and the fourth step executed again are shown in FIG. 8. In thestate of FIG. 7, the neighbor state node is three nodes, i.e., [t=1,n=1], [t=2, n=2], and [t=2, n=3]. The state transition cost cumulativevalue for each of the neighbor state nodes is 7 for [t=1, n=1], 3 for[t=2, n=2], and 5 for [t=2, n=3]. These values are set as they are asthe state transition cost cumulative best values. Therefore, as shown inFIG. 8, the state node [t=2, n=2] newly becomes a fixed node, and itsfixed cost is set to 3.

In this way, the Dijkstra algorithm performs the shortest path search,which sequentially determines one by one from the periphery of the startstate node and incrementally expands the range to the goal state node.

By repeating the above iteration, eventually, one of a set of the goalstate nodes becomes a fixed node, as shown by the state node [t=5, n=5]in FIG. 9. As described above, the state nodes are determined in orderof their smaller state transition cost cumulative best value. In otherwords, the best is preferentially searched. Therefore, at this timingshown in FIG. 9, the path reaching the fixed node [t=5, n=5] is theminimum cost transition path. Thus, the minimum cost transition path inthe time-space network of FIG. 5 can be determined as a path shown asthick arrows of FIG. 9.

The traveling carriage manager 3 determines a traveling schedule basedon the minimum cost transition path obtained. The traveling scheduleincludes a route along which the traveling carriage 2 travels (i.e., thepoint node indicated by each of the state nodes included in the minimumcost transition path) and a timing (i.e., time at which the travelingcarriage 2 is present at each position).

Next, the traveling carriage manager 3 determines a traveling schedulefor each of the traveling carriages 2 which is a subject to which thetransport task is allocated, as described above. Then, the travelingcarriage manager 3 checks whether or not the traveling carriages 2interfere with each other when each of the traveling carriages 2performs automatic travel according to the traveling schedule.

If a collision (interference) between the different traveling carriages2 traveling according to the traveling schedule determined as describedabove has occurred, the traveling carriage manager 3 changes thedetermined traveling schedule for the traveling carriage 2 selectedrandomly among the traveling carriages 2 involved in the collision.

For example, as shown in FIG. 10, consider the case where, in theminimum cost transition path (the path shown in thick dotted line)determined for a certain traveling carriage 2, it is determined that thetraveling carriage 2 collides with another traveling carriage 2 at statenode [t=4, n=2], and state node [t=5, n=3], shown in the double circleof FIG. 10.

In this case, the traveling carriage manager 3 increases the statetransition cost that transitions to each of the state nodes (doublecircles in FIG. 10) in which the collision is detected. Further, thetraveling carriage manager 3 increases the state transition cost thattransitions to the state nodes (circle in bold line in FIG. 10) whosethe point node is same as the point node of the collision state node butthe time differs by a unit of time. The cost increase means a penalty toprevent collisions.

Then, the traveling carriage manager 3 re-obtains the minimum costtransition path in the time-space network where the state transitioncosts are changed as described above. The minimum cost transition pathnewly obtained, as shown by the solid thick arrows in FIG. 10, can avoidcollisions with other traveling carriage 2.

Thus, the traveling carriage manager 3 can efficiently determine thetraveling schedule of the traveling carriage 2 to be allocated for eachof the transport tasks so that the traveling carriages 2 do notinterfere with each other when they perform automatic travel.

As described above, in the traveling schedule determination method ofthis preferred embodiment, the route and the timing of the travelingcarriage 2 which performs automatic travel are determined. In thedetermination method, the route graph is prepared. The route graphrepresents the routes along which the traveling carriage 2 can travel.The route graph includes a set of point nodes, and inter-point edgeseach of which connects between the point nodes. Each of the point node(1), which is the departure point of the traveling carriage 2, and thepoint node (5), which is the arrival point of the traveling carriage 2,can be selected from the point nodes in the route graph. The departuretime, at which the traveling carriage 2 is to depart from the point node(1), and the arrival time, at which the traveling carriage 2 is toarrive at the point node (5), are designated, respectively. In thiscase, in the traveling schedule determination method, the time-spacenetwork is generated. The time-space network represents a procedure forthe traveling carriage 2 traveling from the point node (1) to the pointnode (5). The time-space network includes a set of the state nodes, anda set of the state transition edges each of is connected between thestate nodes. Each of the state nodes represents a state in which thetraveling carriage 2 is present at a certain point node at a certaintime. Each of the state transition edges is connected between the statenodes. The state transition edges include the carriage staying edge 5and the carriage traveling edge 6. The carriage staying edge 5represents a case where the traveling carriage 2 at a certain point nodepresent at a certain time stays at the certain point node until thefollowing time. The carriage traveling edge 6 represents a case wherethe traveling carriage 2 present at a certain point node at a certaintime travels to each of other point nodes connected to the certain pointnode via the inter-point edges at a later time. The carriage travelingedge 6 is defined for each of the point nodes of destination. It ispresupposed that the state node representing a state in which thetraveling carriage 2 is present at the point node (1) at the referencetime (time t=0) is called the starting point state node, the time-spacenetwork is generated originating from the starting point state node. Ineach of the state transition edges, a state transition cost is defined.The state transition cost increases according to a difference of a timet_(σb) corresponding to after transition indicated by the statetransition edge and the second designated time T_(set). In thetime-space network, by using the Dijkstra algorithm, the minimum costtransition path is obtained. The minimum cost transition path is a pathin which a sum of the state transition costs is minimum among paths fromthe starting point state node to any of the state nodes indicating thatthe traveling carriage 2 is present at the point node (5). The route andthe timing of the traveling carriage 2 are determined based on theminimum cost transition path.

As a result, it is possible to obtain efficiently the minimum costtransition path for travel of the traveling carriage from the specifieddesignated loading position P1 to the designated unloading position P2.Additionally, the state transition cost in the state transition edge isset according to a difference of a time t_(σb) after the transitionindicated by the edge and the specified second designated time T_(set).Therefore, it is possible to generate the minimum cost transition pathconsidering the JIT performance so that the traveling carriage 2 arrivesat the designated unloading position P2 at the second designated timeT_(set).

Further, in the traveling schedule determination method of thispreferred embodiment, the third parameter β can be set larger than thefirst parameter α. In this case, the state transition cost is set to belarger, when the time t_(σb) corresponding to after the transitionindicated by the corresponding state transition edge is later than thesecond designated time T_(set), than when it is earlier, even if a timedifference is the same.

As a result, it is possible to greatly reduce the possibility that apath to arrive at the designated unloading position P2 at a time laterthan the second designated time T_(set) is determined as the minimumcost transition path.

Further, in the traveling schedule determination method of thispreferred embodiment, the state transition cost is obtained based on theearliness cost, the tardiness cost, and the staying cost. The earlinesscost is added if the time t_(σb) corresponding to after the transitionindicated by the corresponding state transition edge is earlier than thesecond designated time T_(set). The tardiness cost is added if the timet_(σb) corresponding to after the transition indicated by thecorresponding state transition edge is later than the second designatedtime T_(set). The staying cost is added when the traveling carriage 2stays at any of the point nodes. Each of the first parameter α forweighting of the earliness cost, the second parameter γ for weighting ofthe tardiness cost, and the third parameter β for weighting of thestaying cost can be specified.

By appropriately specifying the first parameter α, the second parametery, and the third parameter β, it is possible to determine a travelingschedule corresponding to the degree of importance with respect to theJIT performance and the transport efficiency respectively.

Further, in the traveling schedule determination method of thispreferred embodiment, a distance between real points represented by thepoint nodes corresponds to a travel distance of per unit time of thetraveling carriage 2.

As a result, the computation of the state transition cost can befacilitated.

Further, in the traveling schedule determination method of thispreferred embodiment, the route and the timing are simultaneously(provisionally) determined by obtaining the minimum cost transition pathfor each of a set of the traveling carriages 2 in which each of thedeparture point node, the arrival point node, the departure time, andthe second designated time T_(set) is designated. If interference occursbetween the traveling carriages 2 in a case where each of the travelingcarriages 2 travels in accordance with the route and the timing aredetermined, the route and the timing are determined again byre-obtaining the minimum cost transition path. The minimum costtransition path is re-obtained after increasing the state transitioncost of the state transition edge corresponding to the interference withthe other traveling carriage 2 for at least one of the interferingtraveling carriages 2.

As a result, the collision avoidance can be easily determined whileconsidering the JIT performance.

Further, in the traveling schedule determination method of thispreferred embodiment, for obtaining the minimum cost transition path,the iteration is repeated after the initial step. In the initial step,in the time-space network, the starting point state node is set to thefixed node and the fixed cost of the starting point state node is set toa predetermined value. The iteration includes the first step, the secondstep, the third step, and the fourth step. In the first step, theneighbor state nodes are obtained. Each of the neighbor state nodes is astate node which is not set to a fixed node, is adjacent to any fixednode, and is connected to the fixed node via the state transition edge.In the second step, with respect to specific neighbor state nodes, thestate transition cost cumulative values for reaching the neighbor statenodes are obtained. The specific neighbor state nodes are neighbor statenodes each of which is adjacent to a new-fixed node and is connected tothe new-fixed node via the state transition edge. The new-fixed node isa node which has become the fixed node newly in the initial step or inthe previous iteration. The state transition cost cumulative value isobtained by adding the cost of the state transition edge to the fixedcost of the new-fixed node. In the third step, with respect to each ofthe neighbor state nodes, the state transition cost cumulative bestvalue is obtained. The state transition cost cumulative best value isthe state transition cost cumulative value that is best among the statetransition cost cumulative values obtained by the second step in theiteration from the first time to the present. In the fourth step, theneighbor state node with the smallest state transition cost cumulativebest value obtained by the third step is set to the fixed node, and thestate transition cost cumulative best value is set to the fixed cost ofthe fixed node. In the method of determining the minimum cost transitionpath, the fixed node and the fixed cost are sequentially obtained byrepeating the iteration. A path in which the fixed cost is the smallestamong the paths reaching the state node indicating that the travelingcarriage 2 is present at the point node (5) is obtained as the minimumcost transition path.

As a result, the minimum cost transition path can be searchedefficiently. Additionally, for example, a traveling schedule that takesinto account the balance between just-in-time performance and the totalcompletion time, which are usually in a trade-off relationship, can bedetermined.

While some preferred embodiments of the present invention have beendescribed above, the above configurations may be modified, for example,as follows.

As the time used for the computation of the state transition cost,instead of the time t_(σb) corresponding to after the transitionindicated by the corresponding state transition edge, the time t_(σa)corresponding to before the transition may be used.

A traveling schedule in which the traveling carriage 2 travels from thedeparture position to the designated loading position P1 may bedetermined as the traveling schedule for traveling from the designatedloading position P1 to the designated unloading position P2. That is,the traveling schedule determination method of the above-describedpreferred embodiment about the traveling schedule for the travelingcarriage 2 from the designated loading position P1 to the designatedunloading position P2 may be similarly applied with respect to thetraveling schedule for the traveling carriage 2 from the departureposition to the designated loading position P1. In this case, the JITperformance for arrival at the designated loading position P1 is alsoconsidered.

After completion of the transport task, the traveling carriage 2 maystay at a current position, may stay at a pre-specified standbyposition, or may wait with traveling along a pre-specified standbyroute. From the viewpoint of ease of traveling schedule generation, itis preferable that the traveling carriage 2 after completing thetransport task stays at a position and waits.

The traveling carriage 2, instead of magnetic tape, may travel along atravel line which is configured from other materials, or may performautomatic travel without a travel line formed from tape or the like.

The traveling carriage 2 is not limited to an unmanned carrier vehiclesuch as AGV. For example, a rail unmanned carrier vehicle (RGV; RailGuided Vehicle), or an overhead traveling vehicle (OHS; Over HeadShuttle) or the like can be used.

A transport area of the traveling carriage 2 may be pre-specified. Inthis case, the traveling carriage 2 may wait at a position where thetransport task has been completed, or may wait at a standby positionpre-specified in the transport area. The traveling carriage manager 3may be provided for each area.

In addition to the transport system 100, a traveling scheduledetermination method of a preferred embodiment of the present inventioncan also be applied to other routing system having a set of vehicles(e.g., automated driving of a vehicle).

While preferred embodiments of the present invention have been describedabove, it is to be understood that variations and modifications will beapparent to those skilled in the art without departing from the scopeand spirit of the present invention. The scope of the present invention,therefore, is to be determined solely by the following claims.

What is claimed is:
 1. A routing determination method of routing forautomated guided vehicles for determining a route and timing of avehicle which performs automatic travel, the method comprising: a)preparing a first graph that represents routes along which the vehiclecan travel, the first graph including a set of point node, andinter-point edges each of which connects between the point nodes so thateach of a departure point node, which is a departure point of thevehicle, and an arrival point node, which is an arrival point of thevehicle, are able to be selected from the point nodes in the firstgraph; b) generating a second graph that represents a procedure of thevehicle traveling from the departure point node to the arrival pointnode when a departure time at which the vehicle is to depart from thedeparture point node and an arrival time at which the vehicle is toarrive at the arrival point node are designated, respectively; whereinthe second graph includes: a set of state nodes each of which representsa state in which the vehicle is present at a certain point node at acertain time; and a set of state transition edges each of which connectsbetween the state nodes, the state transition edges including: a vehiclestaying edge representing that the vehicle present at a certain pointnode at a certain time stays at the certain point node until a latertime; and a vehicle traveling edge representing that the vehicle presentat a certain point node at a certain time travels to each of the otherpoint nodes connected to the certain point node via the inter-point edgeat a later time, the vehicle traveling edge being defined for each ofthe point nodes of destination; presupposing that the state noderepresenting a state in which the vehicle is present at the departurepoint node at a reference time is called a starting point state node,the second graph being generated originating from the starting pointstate node; c) defining a state transition cost that increases accordingto a difference of time corresponding to before or after a transitionindicated by the state transition edge and the arrival time in each ofthe state transition edges; d) obtaining a minimum cost path in which asum of the state transition costs is minimum among paths in the secondgraph from the starting point state node to any of the state nodesindicating that the vehicle is present at the arrival point node byusing the Dijkstra algorithm; and e) determining the route and thetiming of the vehicle based on the minimum cost path.
 2. The routingdetermination method according to claim 1, wherein the state transitioncost is set to be larger when the time corresponding to before or afterthe transition indicated by the state transition edge is later than thearrival time, than when it is earlier, even if a time difference is thesame.
 3. The routing determination method according to claim 1, whereinthe state transition cost is obtained based on: an earliness cost beingadded if the time corresponding to before or after the transitionindicated by the corresponding state transition edge is earlier than thearrival time; a tardiness cost being added if the time corresponding tobefore or after the transition indicated by the corresponding statetransition edge is later than the arrival time; and a staying cost beingadded when the vehicle stays at any of the point nodes; and each of afirst parameter for weighting the earliness cost, a second parameter forweighting the tardiness cost, and a third parameter for weighting thestaying cost are able to be specified.
 4. The routing determinationmethod according to claim 1, wherein a distance between real pointsrepresented by the point nodes corresponds to a travel distance of perunit time of the vehicle.
 5. The routing determination method accordingto claim 1, wherein the route and the timing are simultaneouslydetermined by obtaining the minimum cost path for each of a set of thevehicles in which each of the departure point node, the arrival pointnode, the departure time, and the arrival time is designated; and ifinterference occurs between the vehicles in a case where each of thevehicles travels in accordance with the route and the timing determined,the route and the timing are determined again by re-obtaining theminimum cost path after increasing the state transition cost of thestate transition edge corresponding to the interference with the othervehicle for at least one of the interfering vehicles.
 6. The routingdetermination method according to claim 1, wherein in a method forobtaining the minimum cost path, an iteration is repeated after aninitial step in which the starting point state node in the second graphis set to a fixed node and a fixed cost of the starting point state nodeis set to a predetermined value, the iteration includes: a first step ofobtaining neighbor state nodes each being not set to the fixed node,adjacent to any fixed node, and connected to the fixed node via thestate transition edge; a second step of obtaining state transition costcumulative values for reaching the neighbor state nodes, each of whichis adjacent to a new-fixed node which has become the fixed node newly inthe initial step or in the previous iteration, and is connected to thenew-fixed node, by adding the cost of the state transition edge to thefixed cost of the new-fixed node; a third step of obtaining, withrespect to each of the neighbor state nodes, a state transition costcumulative best value which is the state transition cost cumulativevalue that is best among the state transition cost cumulative valuesobtained by the second step in the iteration from first time to thepresent; and a fourth step of setting the neighbor state node with thesmallest state transition cost cumulative best value obtained by thethird step to the fixed node, and setting the state transition costcumulative best value to the fixed cost of the fixed node; the fixednode and the fixed cost are sequentially obtained by repeating theiteration; and a path in which the fixed cost is smallest among thepaths reaching the state node indicating that the vehicle is present atthe arrival point node is obtained as the minimum cost path.
 7. Acontroller for determining the route and the timing of the vehicle usingthe routing determination method according to claim
 1. 8. A travelingsystem comprising: the controller according to claim 7; and a pluralityof traveling devices to perform automatic travel according to the routeand the timing determined by the controller.